Chapter 8, Problem 67P

Two satellites are in geostationary orbit but in diametrically opposite positions (Fig. 8.17). In order to catch up with the other, one satellite descends into a lower circular orbit (see Conceptual Example 8.1 for a description of this maneuver). How far should it descend if it’s to catch up in 10 orbits? Neglect rocket firing times and time spent moving between the two circular orbits.

FIGURE 8.17 Problem 63